Performance optimization of efficient PbS quantum dots solar cells through numerical simulation

Colloidal quantum dots (CQDs) solar cells are less efficient because of the carrier recombination within the material. The electron and hole transport layers have high impact on the performance of CQDs based solar cells which makes its investigation a very important component of the development of the more efficient devices. In this work, we have tried performance optimization in tetrabutyl ammonium iodide capped lead sulfide (PbS) CQDs (PbS-TBAI) as absorber layers based solar cells by incorporating different hole transport layers (HTLs) to achieve better power conversion efficiency (PCE) in different device architectures by SCAPS—1D numerical simulation software. It was observed from the simulation that the ITO/TiO2/PbS-TBAI/HTL/Au device architecture shows higher power conversion efficiency as compared to the conventional experimentally realized device architecture of ITO/TiO2/PbS-TBAI/PbS-EDT/HTL/Au. The influence of interface defect density (IDD) at the interface TiO2/PbS-TBAI has also been studied where IDD is varied from 1 × 1013 cm−2 to 1 × 1018 cm−2 while keeping the rest of the device parameters intact. The result shows a noteworthy reduction in the PV performance of the device at higher IDD. This modelled device structure provides a new direction toward the experimental realization in high efficiency PbS QDs solar cells.

Device structure and method. So far experimentally successful conventional device architecture of ITO/TiO 2 /PbS-TBAI/PbS-EDT/HTL/Au (architecture-1) as shown in the Fig. 1a, where PbS TBAI is used for the main absorber layer, Titanium dioxide (TiO 2 ) as ETL, and addition layer PbS-EDT for hole extraction which allows holes to pass through it easily due to favorable band alignment with the active PbS-TBAI layer. For this simulation work, the optimum layer thickness of PbS-TBAI and PbS-EDT are taken from the research works 23,24 . For the ETL, we have fixed TiO 2 , as it has shown improvement in the efficiency of the PbS CQDs based solar cell reaching an efficiency of about 13.94% 22 . These two-material layers of ETL and HTL are used to extract the photo-generated electron and hole to the respective electrodes. After calibration for the conventional device architecture, different HTLs, are introduced for analysis. In another device architecture of ITO/TiO 2 / PbS-TBAI/HTL/Au (architecture-2), we have removed the PbS-EDT layer from the conventional architecture and replaced with different HTLs like Copper  www.nature.com/scientificreports/ helps to understand the flow of electron and holes through different layers of the device. The detailed comparative analysis has been made between both the architectures using numerical simulation under AM 1.5G 1 sun spectra. We have done one-dimensional simulation analysis using SCAPS-1D (Solar Cell Capacitance Simulator) tool, developed by Department of Electronics and Information Systems (ELIS) of the University of Gent, Belgium 25 . The SCAPS-1D is very useful tool to simulate device performance before doing real experiment using different parameters of constituent layers 26 . With the help of this SCAPS simulation tool, we can calculate current/voltage characteristics, photovoltaic parameters, quantum efficiencies, carrier density profile, total generation/recombination profile, corresponding energy band diagrams, etc. It works based on the one dimensional Poisson's equation in semiconductors, carrier continuity (electron/hole transport), and the drift-diffusion differential equations. The Poisson's equation is a relationship of the electric field (E) as follows in Eq. (1) where ψ is electrostatic potential, p, n are holes and electrons concentration respectively, q is the elementary charge, N + D and N − A are ionized donor and acceptor dopant carrier concentrations respectively, ε is dielectric constant. The continuity equation for electron and hole are as follows in Eqs. (2) and (3) Charge carriers drift-diffusion equations are indicated by Eqs. (4) and (5).
where D n and D p are electron and hole diffusion coefficient, J n and J p are current densities of electron and holes, G is generation rate (electron and holes) and U n,p is the net recombination rate, μ p , μ n are carrier mobility for hole and electron respectively and E is the electric field. The relationship between diffusion coefficient and carrier mobility is represented by Einstein relation as given in Eq. (6).
where, D(n, p) is diffusion coefficient (m 2 s −1 ), µ is electrical mobility (m 2 V −1 s −1 ), k B is a Boltzmann constant, q is electric charge, and T is absolute temperature (K).
Major attention is given to optimize different parameters in a way through which we can get a clear insight of device performances. The Table 1 shows the different layer parameters that have been used for this simulation process. Some values have been derived from the already published papers while the others have been optimized within the feasible limit after studying the impacts of different structural properties on the device performance.
For realistic simulation and analysis of semiconductor devices, we need to incorporate accurate and reliable optoelectronic properties for all the materials used in the simulation. We have used neutral defect type with 10 -19 cm −2 electron as well as hole capture cross section, reference defect level above the highest E v having energy of 0.6 eV, and total defect density of 2 × 10 14 cm −3 at PbS QD/TiO 2 interface for consideration of interfacial defect density(IDD). Also the role of mobile ions cannot be considered in analysis because of software limitations 27 . The absorption coefficient of PbS used in the simulation as shown in Fig. 1d is obtained from our experimental measurement 28 .

Results and discussion
Influence of doping density. The numerical simulations of PbS CQDs based solar cells of different architectures with different layers were performed based on tabulated parameters collected from different theoretical and experimental research papers. First we have studied the impact of donor doping density of the active layer (PbS-TBAI) on device performances in conventional architecture-1, ITO/TiO 2 /PbS-TBAI/PbS-EDT/MoO 3 /Au. Figure 2a shows the current-voltage characteristics of device with different donor doping density which is varied from 10 14 to 10 19 cm −3 keeping all the other parameters same. It was observed that as the doping increases in the active layer, the device short-circuit current decreases and in the same time open circuit voltage increase. Ultimately device efficiency decreases with the donor doping density. The reverse saturation current decreases as donor doping concentration increases in the active layer. On the other hand, as doping concentration increase the built in potential (V bi ), also increase, because of this open circuit voltage (V OC ) of the device also increase 29,30 . In the case of short circuit current densities (J SC ), at lower doping concentration, photogenerated carrier collection is higher due the presence of wide depletion region. As doping concentration increases, depletion region width decreases, which reduces the carrier collection leading to lower Jsc. To obtain optimized device performance, doping concentration of the different transport layers play very important role especially in carrier  www.nature.com/scientificreports/ transport. Here, in this work we have tried to understand the influence of acceptor doping concentration in conventional device architecture on all of the devices. The acceptor concentration has been varied from 1 × 10 14 cm −3 to 1 × 10 19 cm −3 , while keeping other device parameters fixed, under which, the PV performances using J-V characteristics of all the devices is evaluated and represented in Fig. 2b. It is observed that with the increase in the acceptor doping concentration of the PbS-EDT, the performance of the device has improved very significantly as shown in Fig. 3a-d. A small change in the J SC of the device is observed (Fig. 3b); however, the V OC remains almost constant about 0.77 V and fill factor (FF) increase significantly as the acceptor doping of the PbS-EDT is increased as shown in Fig. 3a and c respectively. FF is mainly affected by the series resistance of the device. The total series resistance of the device is combination of the resistance of individual layers and their associated interfaces and metal-semiconductor contacts contribute into it. As the PbS-EDT doping is increased, the resistivity of PbS-EDT decreases and hence supports the hole flow from the absorber layer to HTL easily. The higher built-in potential and electric field with doping of 1 × 10 19 cm −3 are validated by a higher slope of quasi-Fermi energy levels, this higher slope results in improved V OC . The fill factor of the device increases with increase in acceptor doping density from 68.03% at 10 14 cm −3 to 74.70% at 10 19 cm −3 , which ultimately helps holes to move easily to the contact electrode as shown in Fig. 3c. The efficiency of the solar cells is directly related to the FF, as the FF increase, the efficiency of the device increases and hence the cell achieved 16.26% efficiency at 10 19 cm −3 doping density as shown in Fig. 3d. Further, the conventional device architecture has been simulated with varying the interface defect density at TiO 2 /PbS-TBAI interface. The effect of interface variation can be observed at light entering side of the device i.e. at TiO 2 /PbS-TBAI interface. The effect of variation in interface defect density (IDD) where light reaches later after the main absorber layer is negligible 22 . The defect density at TiO 2 /PbS-TBAI layer is varied from 10 13 to 10 18 cm −3 by keeping all other parameters fixed. Figure 2c and d show the J-V characteristics and correspoing QE spetra for different interface defect density. It was observed that there exists significant decrease in charge carrier extraction due to increase in defect density within 650 nm wavelength, beyond that the changes are insignificant. As the light enters the device through TiO 2 layer side, most of the high energy photons get abosrbed at the TiO 2 /PbS-TBAI interface and create electron-hole pairs. But due to higher defect density, the recombination of generated charge carrier is also higher at the TiO 2 /PbS-TBAI interface. All the three parameters V OC , Jsc and FF reduces as the IDD increases with same nature which is shown in the Fig. 4a-d. This results in reduction of the device efficiency from 17.81% at IDD 10 13 cm −3 to 13.59% at IDD 10 18 cm −3 which clearly shows increased carrier losses due to increment in IDD.
Further we have examined the performance of devices having architecture-1 (ITO/TiO 2 (80 nm)/PbS-TBAI (220 nm)/PbS-EDT (45 nm)/HTL (10 nm)/Au) by having different HTLs over the architecture-2 (ITO/ TiO 2 (80 nm)/PbS-TBAI (220 nm)/HTL/Au).  Fig. 5a. Among five different HTLs, it has been observed that the conventional device with MoO 3 as HTL has stable performance with acceptor density variation due to better passivation with the previous PbS-EDT layer. Other HTLs converge towards better device efficiency with increase in acceptor donor density of active layer due to improvement in charge carrier with increase in doping density. Interestingly, at low doping density, the device which has CuO as HTL starts with poor performance and efficiency nearly about 5% due to low J SC and FF resulting into poor device performance. But at large acceptor doping densities such as 10 19 cm −3 , the efficiency of this device is found to reach up to the same level as that of devices with other HTLs. This must be due to large concentration of holes at large doping density of the HTL hence the performances of the device improved.
Further, with the simulation we have also tried to investigate performance of devices with different HTLs without PbS-EDT layer before PbS-TBAI layer i.e. the architecture ITO/TiO 2 (80 nm)/PbS-TBAI (265 nm)/HTL (10 nm)/Au (Architecture-2). To keep the effective thickness of the device constant in both architectures, we have taken the thickness of PbS-TBAI layer as 265 nm in the architecture-2. The variation of performances of the devices with increase in doping density of HTL from 10 14 to 10 19 cm −3 incorporating different HTLs is shown in Fig. 5b. We observed similar trend of increase in V OC , Jsc and FF which is resulting in increase in overall efficiency as we move ahead from low acceptor density towards high acceptor doping density. Also the conventional device architecture has been included in graph whose overall efficiency is lower as compared to other devices due to lower J SC and FF even if the device has stable V OC over variation in doping density. Also, there is surprisingly improved performance in CuO based HTL device as compared to previous architecture-1, the efficiency in this architecture is found to be increased from 6 to 15% at 10 15 cm −3 doping density. This improvement is due to improved collection of charge carriers across the layers of the device which is due to the absence of the PbS-EDT layer. The removal of PbS-EDT layers makes the active layer to come in direct engagement with the CuO HTL which is enhancing the current density and hence the device efficiency.
The   Table 2. It is quite clear that V OC and J SC of the all the devices with different HTLs are almost similar and only variation in FF of the devices with different HTLs. The J sc variation due to different HTLs is further confirmed from the quantum efficiency curve in the Fig. 5d. The device with MoO 3 HTL device shows highest power conversion efficiency of 16.43% with V OC of 0.783 V and J sc of 28.50 mA cm −2 and FF of 73.61%, the corresponding QE spectra also shows similar trend as like J-V curve.
If we compare the device performances between ITO/TiO 2 (80 nm)/PbS-TBAI (220 nm)/PbS-EDT (45 nm)/ HTL (10 nm)/Au)-architecture 1 by having different HTLs and ITO/TiO 2 (80 nm)/PbS-TBAI (220 nm)/HTL/ Au-architecture 2, it was found that except CuI as HTL, all other devices with architecture-2 performed better in comparison to the devices with architecture-1. The comparative variation in efficiency of devices of architecture-1 and architecture-2 with IDD also shows that the device having HTLs without PbS-EDT layer (architecture-2) performs better than the architecture with PbS-EDT layer (Architecture-1). Therefore, from  www.nature.com/scientificreports/ this simulation work, it is clear that device architecture 2 which utilizes HTLs without PbS-EDT layer in between the active PbS-TBAI layer and HTL is much better as compared to conventional device architecture-1.

Conclusion
In summary, the performance of PbS CQDs based solar cell in different device architectures have been investigated by numerical simulation method. A detailed comparative study has been carried out to analyze the impact of different hole transport layers on device performance. It was observed that the ITO/TiO 2 /PbS-TBAI/HTL/Au device architecture (Architecture-2) in which the PbS-EDT layer has been replaced with different HTLs is superior to the most conventional device architecture of ITO/TiO 2 /PbS-TBAI/PbS-EDT/HTL/Au (Architecture-1). The device with MoO 3 HTL showed the highest power conversion efficiency of 16.43% with V OC of 0.783 V and Jsc of 28.50 mA cm −2 and FF of 73.61%. Besides variation in doping density, the performance of the devices has also been examined with varying defect density at the interface PbS-TBAI/TiO 2 and a similar trend of decline in performance has been observed. Results carried out in the current study can be used more widely to engineer the device architectures with better HTL by selectively choosing different HTLs and also their variation with doping density and interface defects to uplift the performance of PbS CQD based solar cells.

Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.